1. Field of the Invention
The present invention relates to a method and apparatus for digital quadrature lock-in detection in magnetic resonance.
2. Description of Related Art
Analog Quadrature Detection
FIG. 7 is a block diagram showing an example of the configuration of an NMR (nuclear magnetic resonance) spectrometer. The spectrometer has a pulse sequencer 1 producing RF (Radio Frequency) pulses that enter a direct digital synthesizer (DDS) daughter card 2, where given processing is performed. The daughter card 2 consists of a digital direct synthesizer (DDS) 2a, a D/A (digital to analog) converter (DAC) 2b, and a low-pass filter 2c. The DDS daughter card 2 produces pulses of 9 to 12 MHz.
The RF pulse then enters a following transmitter 3. The transmitter 3 includes a mixer 3a and an attenuator (ATT) 3c for attenuating the output from the mixer 3a, which mixes the output from the DDS daughter card 2 and the output from a distributor 3b. The output from the attenuator 3c is amplified by a following power amplifier 4 and applied to a probe 6. An NMR signal detected by the probe 6 is passed to an OBS receiver 10 via a duplexer (DPLX) 5 and a preamplifier 7.
In the OBS receiver 10, the NMR signal is mixed with a locally generated (LO) signal from a frequency synthesizer (FSY) 20 by an image reject mixer (IRM) 11. The signal from the synthesizer 20 is selected by an FSY selector 12 and applied to the image reject mixer 11, where the signal is mixed with the signal from the preamplifier 7. The output signal from the mixer 11 has an intermediate frequency (IF). The output from the image reject mixer 11 is passed through a bandpass filter 13 that passes only frequencies of 9 to 12 MHz. The output signal from the filter 13 is split into two by a splitter 14.
An intermediate frequency (IF) is generated by a digital direct synthesizer (DDS) 15 and passed to mixers 17a and 17b through D/A (Digital to Analog) converters (DACs) 16a and 16b, respectively. The two signals from the splitter 14 are mixed with intermediate-frequency (IF) signals which are 90° out of phase at the mixers 17a and 17b, respectively. The output signals from the mixers 17a and 17b are passed through AF (audio frequency) filters 18a and 18b, respectively, to remove unwanted RF components. The output signals from the filters 18a and 18b are converted into digital signals by A/D (Analog to digital) converters (ADCs) 31a and 31b, respectively. The resulting data are temporarily held in a signal processing portion 32. One of the two digital signals is herein referred to as a real part, while the other is referred to as an imaginary part. In this case, any one of them may be a real part.
Digital Quadrature Detection
FIG. 8 is a block diagram showing a second example of the configuration of an NMR spectrometer. Like components are indicated by like reference numerals in both FIGS. 7 and 8. In analog quadrature detection shown in FIG. 7, two signals, which originate from the digital direct synthesizer (DDS) 15 and are applied as IF signals to the mixers, are out of phase. In contrast, in the configuration shown in FIG. 8, one phase signal is converted into an analog signal by a DAC 16b and then mixed with an NMR signal at a mixer 17b. However, when the signal is accepted into the ADC 31b, it is necessary that the signal be oversampled at a frequency more than twice as high as the required spectral width SW.
FIG. 1 is a conceptual diagram illustrating digital quadrature detection underlying the concept of the present invention, and depicts subsequent processing on digital data obtained by the signal processing portion 32. Time domain data stored in a data buffer 40 are copied as two data sets. One data set is multiplied by sin Ωt, while the other is multiplied by cos Ωt. The products are passed through digital low-pass filters (D-LPFs) 42a and 42b, respectively, and stored in data buffers 2R and 2I, respectively. The stored data sets are taken as real and imaginary data, respectively. The data buffers 2R and 2I are indicated by 43a and 43b, respectively.
Summary and Principle of Lock-In Amplifier
Summary and principle of a lock-in amplifier are next described. FIG. 2 illustrates lock-in detection and the principle of a lock-in amplifier. It is assumed that an observed signal consists of a single frequency. The observed signal can be given by sin (ωt+α). A case is discussed in which a reference signal is prepared and brought into coincidence with the observed signal in terms of frequency or the frequency is swept for coincidence.
If the coincidence is achieved, the reference signal can be given by sin (ωt+β). If the product of the reference signal sin (ωt+β) and observed signal sin (ωt+α) is calculated by a multiplier 45, formulas of products and sums of trigonometric functions state that the output from the multiplier 45 is given bycos(2ωt+α+β)−cos(α−β)Of this formula, the former term is an AC component varying with time. The latter term is a DC component not varying with time.
Only the DC component −cos (α−β) can be obtained by cutting off RF components by a low-pass filter (LPF) 46 having a cutoff frequency lower than 2ω and passing only low-frequency components. Generally, noise can be blocked by cutting off the region other than a band of interest by a filter. In the case of this lock-in amplifier, noise components located outside a band of reference signal ±about cutoff frequency can be blocked because the cutoff frequency of the low-pass filter 46 can be set to a very low frequency. As a result, low-noise detection is enabled. Hence, this lock-in amplifier is often used for high-sensitivity measurements. This detection system is referred to as the lock-in amplifier.
Quadrature Lock-In Detection
Quadrature lock-in detection is next described. The reference signal shown in FIG. 2 is sin (ωt+β). The phase is not definite. The signal cannot be observed depending on the value of β and thus the phase of the observed signal cannot be known. (Usually, the phase is to be optimized.) To avoid this, a quadrature lock-in amplifier is available.
FIG. 3 illustrates quadrature lock-in detection. Like components are indicated by like reference numerals in both FIGS. 2 and 3. In this quadrature lock-in amplifier, an observed signal is multiplied by reference signals by means of multipliers 45 and 45a, respectively. The observed signal is split into two parts which are multiplied by reference signals which are 90° out of phase (e.g., sine wave and cosine wave, respectively). The products are passed through low-pass filters 46 and 46a, respectively, in the same way as in the above-described example. They are observed as two out of phase signals. Where the reference signal is sin (ωt+β), the DC output signal from the low-pass filter 46 is −cos (α−β). Where the reference signal is cos (ωt+β), the DC output signal from the low-pass filter 46a is sin (α−β).
Thus, signals can be received with at least one of the two channels without depending on the phases of the observed signal α and reference signal β. Furthermore, the phase of the observed signal relative to the reference signal can be known. Note that symbols and coefficient ½ are omitted in FIGS. 2 and 3.
Digital Lock-In Detection
Digital lock-in detection is next described. The above-described lock-in amplifier can be digitized. FIG. 4 illustrates digital lock-in detection. An analog observed signal sin (ωt+α) is entered. An A/D converter 47 converts the observed signal into a sequence of digital numerical values varying with time. The converted observed signal is input to one input terminal of a multiplier 48. A digital reference signal sin (ωt+α) is input to the other input terminal of the multiplier 48.
The reference signal is multiplied by a sequence of numerical values corresponding to a sine wave. The obtained sequence of numerical values is passed through a digital low-pass filter 49. In this way, a sequence of digital numerical values −cos (α−β) corresponding to a DC signal can be obtained. A lock-in amplifier that has been digitized in this way can also be available. In addition, a digital quadrature lock-in amplifier can also be achieved by combination with the circuit shown in FIG. 3.
An apparatus of this kind is known as disclosed, for example, in Japanese Patent Laid-Open No. H10-99293 (paragraphs 0008-0012; FIGS. 1 and 2). In this technique, real and imaginary part data are obtained by DPSD complex detection based on a 4-fold oversampling technique, and the difference in amplitude between the real and imaginary part data is reduced. Furthermore, a technique regarding improvement of a quadrature phase detection technique for performing quadrature phase detection of a signal from the receiver coil of a magnetic resonance imaging apparatus is known (see, for example, Japanese Patent Laid-Open No. H5-317285 (paragraphs 0016-0034; FIGS. 1 and 3).
Another technique for reconstructing a magnetic resonance signal is also known as disclosed, for example, in Japanese Patent Laid-Open No. H4-357937 (paragraphs 0015-0022; FIG. 6). The magnetic resonance signal is separated into two signals by detection using two reference waves having resonance frequencies that are 90° out of phase. The detected signals are Fourier transformed and corrected in the Fourier space, thus removing noise. Then, the signal is reconstructed.
In the case of the aforementioned analog quadrature detection, two different A/D converters (ADCs) are used. Therefore, it is difficult to make uniform the converters in gain and DC offset. Accordingly, there is the problem that image artifacts and center glitch (artifacts caused by frequency offset) tend to be produced. Furthermore, generally, in magnetic resonance phenomena (especially, nuclear magnetic resonance phenomena such as NMR and MRI), quite weak energies are treated. Therefore, the sensitivity is low in principle. Accordingly, improving the sensitivity is quite important in developing magnetic resonance apparatus.